I have 02 odyssey when i start the van engine start but stop immediately

When the car dies all the lights come on but when i go to shut the ignition off it blinks like normal, van starts and runs just dies after 5 seconds. Went out there and tried again and i got it running for a few seconds but it died again and when i tried to start it again the battery was dead, shouldnt the alternator kicked on and charged the battery even a little?

"it blinks like normal' -meaning if you were to turn the key to 'run' NOT start position , the immobilizer light comes on for a few seconds then goes off and stays off? --IF it blinks continuously , there is a problem with it. Need to get battery FULLY charged first , now (at this point I wouldn't recommend just a jump start).